1.) water is flowing through a horizontal pipe of varying crosection, the diameter is 12.0 cm at a pressure of 8.0x10^4 Pa. at section 2, the pipe has a diameter of 6.0 cm and the pressure is 6.0x10^4 Pa. find the speed of water through section 1 and 2 (HINT: Use the continuity equation and bernoullis eqn.)

To find the speed of water through sections 1 and 2, we can use the continuity equation and Bernoulli's equation. Here's how you can approach the problem:

1. Use the continuity equation: The continuity equation states that the mass flow rate of an incompressible fluid is constant along a pipe. It is given by the equation: A1v1 = A2v2, where A1 and A2 are the cross-sectional areas of the pipe at sections 1 and 2 respectively, and v1 and v2 are the speeds of water at sections 1 and 2 respectively.

2. Find the cross-sectional areas: Given that the diameter of the pipe at section 1 is 12.0 cm, you can calculate the radius (r1) as r1 = 12.0 cm / 2 = 6.0 cm = 0.06 m. The area (A1) is then π(r1)^2.

3. Calculate the speed at section 1: Since you know the pressure (P1) at section 1 is 8.0x10^4 Pa, you can use Bernoulli's equation, which relates the pressure, density (ρ), and speed of fluid, to calculate the speed (v1). The Bernoulli equation is given by: P + 0.5ρv^2 + ρgy = constant, where P is the pressure, ρ is the density of the fluid (which you can assume as constant), v is the speed of flow, g is the acceleration due to gravity, and y represents the elevation. In this case, we can assume the pipe is horizontal, so the y term is zero. Plug in the values for P1 and solve for v1.

4. Find the cross-sectional area at section 2: Similar to step 2, find the radius (r2) of the pipe at section 2 using the given diameter of 6.0 cm, and calculate the cross-sectional area A2.

5. Calculate the speed at section 2: Use the same Bernoulli's equation as in step 3, but this time with the pressure (P2) at section 2 (which is given as 6.0x10^4 Pa) to calculate the speed (v2).

By following these steps, you should be able to find the speeds of water through sections 1 and 2.